According to the sociologist Stanley Lieberson, African Americans have traditionally been more willing to use "invented" names compared to White Americans, but this didn't really take off until the 1960s when there was a large-scale movement among African Americans to try to distinguish themselves culturally. As Liberson argues:
In fact, as we shall see, the timing of this development suggests an influence stemming from the intense social and political changes beginning in the 1960s, a period marked by intensified African-American social protest, the development of the Black Power movement, a renewed emphasis on a distinctive and valued African-American culture, and black separatism.^1
He cites one specific example: by 1989 in Illinois, 29% of girls born to African Americans and 16% of boys had unique names, compared to just 5% of white girls and 3% of white boys.^2
As far as where the names come from, Islamic culture was a big influence (e.g. with Cassius Clay --> Muhammad Ali). In addition, things like Roots were also an influence: the year the show aired (1977), Kizzy (one of the characters) was the 17th most-common name among African American girls (again in Illinois).^3 He also suggests that Marcus Garvey was an influence for the name "Marcus" becoming more popular; the name was 164th in popularity for black males born in 1956, but was 5th by 1983.^4 Given the timing (Garvey died in 1940), this makes me think its popularity ties back in with the political changes described above.
He later notes the increase (around this same timeframe) of names beginning with La. He argues that a couple things account for this: the overall rise in unique names means new patterns will emerge, plus the La- names tended to be based on already-popular names.^5 But this is the result, rather than the cause, of African Americans' greater propensity to choose unique names.
Later, he notes an interesting difference in Black vs. White girls' names in Augusta, Georgia in 1937: Black girls' names were far more likely to end in a vowel, and may have been a more nickname-type form. He argues that this could be because it was common during this time to refer to Blacks by their first name, and that "names with vowel endings, particularly nicknames ending with ee, are often less assertive and carry a childlike connotation." He also notes that using nicknames implies a degree of intimacy and "less social distance," and so Blacks' maintaining use of nicknames for longer showed a societal pressure to diminish them.^6
Ultimately, he argues that Black names reflected race relations, "both actual and ideological, from the earliest forced migration under slavery through today."^7
edit for typo, thanks to /u/GoodGuyGoodGuy
^1 Stanley Lieberson, A Matter of Taste: How Names, Fashions, and Culture Change at 76.
^2 Ibid.
^3 Ibid.
^4 Id. at 77.
^5 Id. at 122-126.
^6 Id. at 207.
^7 Ibid.
(Apologies for using legal-style citation, but it's what's ingrained at this point.)
If OP and the mods are OK with this, I'd like to add a sub-question to the topic: Are names in the African American community actually of African origin? I got into this discussion with a coworker from Ghana (I'm from the USA but living in Europe) asking me about this and I had grown up assuming such names were of African origin but never had any proof. He found the whole trend in the US quite interesting and in Ghana the naming tradition among a large swath of the population is quite unique.
I have a sub question to this: Have unique surnames arisen in any other former slave or immigrant populations in other countries? To my knowledge, they haven't. The afro-brazilian population doesn't do it, I don't think. Nor do the black communities in France or England. Is this phenomena unique to the United States?